On Hurwitz Spaces of Coverings with One Special Fiber
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چکیده
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Riemann, Hurwitz, and Branched Covering Spaces
We will consider spaces with nice connectedness properties, and the groups that act on them in such a way that the topology is preserved; we consider looking at the symmetry groups of a surface of genus g. Restricting our view to finite groups, we will develop the concept of covering spaces and illustrate its usefulness to the study of these group actions by generalizing this development to the...
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The Hurwitz space is a compactification of the space of rational functions of a given degree. We study the intersection of various strata of this space with its boundary. A study of the cohomology ring of the Hurwitz space then allows us to obtain recurrence relations for certain numbers of ramified coverings of a sphere by a sphere with prescribed ramifications. Generating functions for these ...
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